What are the meanings of the epigraphs in The Secret Life of Bees?

Each of the epigraphs offers a comment about "the secret life of bees" that also serves as a focusing lens for the chapter it precedes. By reflecting on the human implication of the epigraph concerning bees, the reader can find a deeper significance in the plot unfolding.
The first epigraph addresses "queenlessness," and Lily is clearly in need of a communal "hive" so that she can grow into her potential. As she learns from the Boatwright sisters how to care for bees, she also learns how to care for herself and others. Chapter 2 discusses "scout bees," and Lily and Rosaleen go in search of Tiburon and the Black Mary. When Lily and Zach begin to fall in love and Lily awakens to her maturing sexual self, the chapter is preceded by an epitaph about the sexual behavior of bees.
In chapter 6, we read,

The Queen must produce some substance that attracts the workers and that can be obtained from her only by direct contact. This substance evidently stimulates the normal working behavior in the hive. This chemical messenger has been called "queen substance." Experiments have shown that the bees obtain it directly from the body of the queen.

This connects to the chapter, which concerns a Daughters of Mary service in which participants feel a great release and empowerment when they touch the statue.
We can judge Lily's growth by the last epigraph. Lily has not finished her progress, and she is still trying to reconcile herself to the memory of her mother, but she seems ready to advance into adulthood secure in wisdom she has gained with the Boatwrights. Like the first one, this epigraph discusses a hive whose queen has died. The difference here is that, instead of ending on "queenlessness," this last epigraph suggest hope for a dynamic future when the new queen arrives. One senses that Lily is ready to accept the mantle of being her own queen bee.

Each epigraph in The Secret Life of Bees connects in some way to the chapter it heads. Some of those examples are simple and straightforward, but most are metaphorical. They speak to the motif of bees as an allegory for the life of this little society that we're watching from the outside—much as humans must do when observing bees in their natural habitats.
A strong example of this is the epigraph in chapter four. Very simply, the epigraph describes honeybees and their social colony. It highlights a strong central female figure who acts as figurehead for all other workers. It also mentions that male bees are more or less absent.
This model is very strongly reflected in the Boatwright home that Lily and Rosaleen are about to encounter. August Boatwright is very clearly the queen bee described in the epigraph. She is even called "Mistress of the Bees" by Lily (68). Her sisters demonstrate worker-like qualities, and males are conspicuously missing from the home—at least at the beginning.
The connection between the epigraph and the chapter it precedes is replicated throughout the text.